Rank and crank moments for overpartitions

35Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

Abstract

We study two types of crank moments and two types of rank moments for overpartitions. We show that the crank moments and their derivatives, along with certain linear combinations of the rank moments and their derivatives, can be written in terms of quasimodular forms. We then use this fact to prove exact relations involving the moments as well as congruence properties modulo 3, 5, and 7 for some combinatorial functions which may be expressed in terms of the second moments. Finally, we establish a congruence modulo 3 involving one such combinatorial function and the Hurwitz class number H (n). © 2008 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Bringmann, K., Lovejoy, J., & Osburn, R. (2009). Rank and crank moments for overpartitions. Journal of Number Theory, 129(7), 1758–1772. https://doi.org/10.1016/j.jnt.2008.10.017

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free